Semitone Calculator – Notes, Intervals and Frequency Ratios
The Semitone Calculator helps musicians and music students understand semitone intervals between musical notes, calculate frequency ratios, and identify note names across octaves. Convert between note names, semitone distances, and frequency values. Useful for composers, guitarists, pianists, and music theory students. Formula based on the equal temperament tuning system with A4 = 440 Hz as the reference pitch. For professional pitch analysis, verify with a chromatic tuner or digital audio workstation.
Formula
This calculator transforms the provided inputs into the requested outputs using standard domain equations.
Quick Tip
Change one input at a time to see which variable influences the result most.
Working with intervals, note frequencies, or transposition in music? Enter two notes or a semitone count and get the frequency ratio, note names, and interval name — instantly.
Featured Answer
Q: How many semitones are between notes and what is the frequency ratio?
A: In equal temperament, each semitone has a frequency ratio of 2^(1/12) ≈ 1.0595. An octave contains 12 semitones and doubles the frequency. C4 (middle C) is 261.63 Hz. One semitone up is C#4 at 277.18 Hz. Twelve semitones up is C5 at 523.25 Hz — exactly double. Use this calculator to find semitone distances, note names, and frequencies for any starting note.
How to Use Semitone Calculator
- Select or enter a starting note — such as C4, A3, or G#5.
- Enter a semitone count — the number of semitones to move up (positive) or down (negative).
- The calculator shows the resulting note name, frequency, and interval name.
What is a Semitone?
A semitone is the smallest interval in standard Western music. It is the distance between two adjacent notes on a piano keyboard — for example, from C to C#, or from E to F.
In equal temperament tuning, every semitone has the same frequency ratio: 2^(1/12) ≈ 1.0595. This means each semitone multiplies the frequency by approximately 1.0595.
Twelve semitones make one octave. One octave exactly doubles the frequency. So moving 12 semitones up from A4 (440 Hz) gives A5 (880 Hz).
Common intervals by semitone count:
- 1 semitone = Minor second
- 2 semitones = Major second
- 7 semitones = Perfect fifth
- 12 semitones = Octave
Example: Starting note A4 (440 Hz), moving up 7 semitones.
| Field | Value |
|---|---|
| Starting Note | A4 — 440 Hz |
| Semitones | +7 |
| Resulting Note | E5 |
| Frequency | 659.26 Hz |
| Interval Name | Perfect fifth |
Semitones in Music: Intervals, Frequencies, and Note Names
Why Semitone Calculator Matters
Music theory involves a lot of mental arithmetic. Transposing a melody up by a fifth. Finding the frequency of a note two octaves above middle C. Building a chord by stacking specific intervals.
This calculator handles those calculations instantly. It removes the mental maths so you can focus on the music.
For students learning interval theory, it also provides the interval name alongside the note and frequency — reinforcing the connection between mathematical ratios and musical names.
How Semitone Frequency Is Calculated — Step by Step
- Start with the reference frequency: A4 = 440 Hz (international standard).
- Find the semitone distance from A4 to the starting note: n semitones.
- Calculate starting note frequency: f = 440 × 2^(n/12).
- Add the desired semitone offset to n.
- Calculate resulting note frequency: f_result = 440 × 2^((n + offset)/12).
- Identify the note name from the semitone position within the 12-note chromatic scale.
Semitone Intervals Reference
| Semitones | Interval Name | Example |
|---|---|---|
| 0 | Unison | C to C |
| 1 | Minor second | C to C# |
| 2 | Major second | C to D |
| 3 | Minor third | C to Eb |
| 4 | Major third | C to E |
| 5 | Perfect fourth | C to F |
| 7 | Perfect fifth | C to G |
| 9 | Major sixth | C to A |
| 12 | Octave | C to C (next) |
Common Mistakes to Avoid
- Confusing semitones and tones. One tone = 2 semitones. A major scale has tones and semitones in a specific pattern: T-T-S-T-T-T-S.
- Forgetting that equal temperament is an approximation. Just intonation produces slightly different ratios for some intervals.
- Misidentifying enharmonic equivalents. C# and Db are the same pitch but written differently depending on the musical context.
- Not specifying octave when naming notes. C4 and C5 are an octave apart. Always include the octave number for clarity.
- Applying semitone counts in the wrong direction. Positive semitone values go up in pitch. Negative values go down.
When to Use This Calculator
Use this tool when transposing music to a new key. Count how many semitones separate the original key from the target key and apply that offset to all notes.
Also useful for guitar players building chords in alternate tunings, for composers verifying frequency relationships between notes, and for students learning to identify intervals by ear and by name.
For general mathematics involving logarithms and exponents, the Antilog Calculator handles the underlying maths. For music theory at a broader level, this calculator covers the foundational pitch calculations.
Pro Tips
Resulting note name — use this when transposing. If you move every note in a melody up by 5 semitones, this shows what each new note name will be.
Frequency — useful for electronics and audio engineering. When setting oscillator frequencies or checking tuning against a reference signal, exact Hz values matter.
Frequency ratio — 2^(1/12) per semitone. Memorise this. It is the core of equal temperament and comes up in both music theory and acoustic physics.
Interval name — connecting semitone counts to named intervals reinforces music theory. Seven semitones is always a perfect fifth, regardless of the starting note.
Important Assumptions and Limitations
This calculator uses equal temperament tuning with A4 = 440 Hz as the concert pitch reference. Just intonation and other tuning systems produce slightly different frequency values for the same interval names. Results are mathematically precise for equal temperament. Calculation method reviewed against standard equal temperament frequency formula references.
Frequently Asked Questions
Find answers to common questions about Semitone Calculator
A semitone is the smallest interval in standard Western music. It is the pitch difference between two adjacent notes on a piano — for example, from C to C#, or from B to C. In equal temperament tuning, every semitone has the same frequency ratio of 2^(1/12) ≈ 1.0595. Twelve semitones make one octave, which doubles the frequency.
Use the equal temperament formula: f = 440 × 2^(n/12), where n is the number of semitones from A4 (440 Hz). For C4 (middle C), n = −9, so f = 440 × 2^(−9/12) ≈ 261.63 Hz. For a note 7 semitones above A4 (E5): f = 440 × 2^(7/12) ≈ 659.26 Hz. This calculator applies the formula for any starting note.
The calculator is mathematically precise for equal temperament tuning with A4 = 440 Hz. Frequencies are calculated using the exact 2^(1/12) ratio. Interval names follow standard Western music theory conventions. For alternative tuning systems such as just intonation or meantone temperament, the frequency values will differ from equal temperament outputs.
Interval name is the standard Western music theory label for the pitch distance between two notes. It is determined by the semitone count. Two semitones is a major second. Four semitones is a major third. Seven semitones is a perfect fifth. Twelve semitones is an octave. Learning these connections between semitone counts and interval names is fundamental to music theory.
Use it when transposing music to a new key — count the semitone distance between keys and apply it uniformly to all notes. Use it when building chords or scales by stacking specific intervals. Use it when learning music theory to connect interval names with frequency ratios. Also useful for audio engineers tuning instruments to specific reference frequencies.
A perfect fifth spans 7 semitones. Moving 7 semitones up from any note gives the note a perfect fifth above it. From C it gives G. From A it gives E. From D it gives A. The perfect fifth has a frequency ratio of 2^(7/12) ≈ 1.4983 in equal temperament — very close to the pure ratio of 3:2 (1.500) in just intonation.
Yes. First determine how many semitones separate the original key from the target key. For example, transposing from C major to E major requires moving up 4 semitones. Apply that 4-semitone offset to every note in the song. This calculator shows what each transposed note name and frequency will be for any starting note and semitone offset.
In equal temperament, adjacent semitones have a frequency ratio of 2^(1/12) ≈ 1.05946. This means each semitone up multiplies the frequency by approximately 1.0595. Moving 12 semitones (one full octave) multiplies the frequency by 2^(12/12) = 2 exactly — doubling the frequency. This equal ratio across all semitones is the defining property of equal temperament tuning.